Delocalized and Resonant Quantum Transport in Nonlinear Generalizations of the Kicked Rotor Model

Abstract

We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked Rotor. We consider two different models, in which the nonlinear term acts either in the position or in the momentum representation. We numerically investigate the modifications induced by the nonlinearity in the quantum transport in both localized and resonant regimes and a comparison between the results for the two models is presented. Analyzing the momentum distributions and the increase of the mean square momentum, we find that the quantum resonances asymptotically are very stable with respect to the nonlinear perturbation of the rotor's phase evolution. For an intermittent time regime, the nonlinearity even enhances the resonant quantum transport, leading to superballistic motion.

arXiv comment8 pages, 10 figures; to appear in Phys. Rev. E

References in corpus (13)

• Theory of Bose-Einstein condensation in trapped gases
• Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1-D optical lattices
• Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
• Experimental evidence of dynamical localization and delocalization in a quasi-periodic driven system
• Quantum resonances and decoherence for delta-kicked atoms
• Nonlinear Matter Wave Dynamics with a Chaotic Potential
• Transition to Instability in a Kicked Bose-Einstein Condensate
• A classical scaling theory of quantum resonances
• Decoherence as a Probe of Coherent Quantum Dynamics
• Current relaxation in nonlinear random media
• Superballistic spreading of wave packets
• Nonlinearity effects in the kicked oscillator
• Effects of a nonlinear perturbation on dynamical tunneling in cold atoms

Cited by in corpus (13)

• Resonant nonlinear quantum transport for a periodically kicked Bose condensate
• Interactions destroy dynamical localization with strong and weak chaos
• Dynamics of the mean-field interacting quantum kicked rotor
• Experimental verification of a one-parameter scaling law for the quantum and "classical" resonances of the atom-optics kicked rotor
• Wave interactions in localizing media - a coin with many faces
• Second-order, number-conserving description of non-equilibrium dynamics in finite-temperature Bose-Einstein condensates
• Dynamical instability in kicked Bose-Einstein condensates: Bogoliubov resonances
• Macroscopic Quantum Self-Trapping in Dynamical Tunnelling
• Coherence and Instability in a Driven Bose-Einstein Condensate: A Fully Dynamical Number-Conserving Approach
• The role of quasi-momentum in the resonant dynamics of the atom-optics kicked rotor
• Nonlinear Lattice Waves in Random Potentials
• Sensitivity to the initial state of interacting ultracold bosons in disordered lattices
• An $\epsilon$-pseudoclassical model for quantum resonances in a cold dilute atomic gas periodically driven by finite-duration standing-wave laser pulses